Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
380 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #26011246 | C2 | semidirect |
| 4. #26011245 | C2 | semidirect |
| 5. #336×C173 | C2 | semidirect |
| 29. C2×C4×D173 | C8 | semidirect |
| 106. C173 | #1817 | semidirect |
| 112. #336 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×D173 | 2 |
| C2×#19149591 | 2 |
| #26011246 | 2 |
| #26011245 | 2 |
| #336×C173 | 2 |
| #1817 | 173 |